Solving Exponential Equations GraphicallyGiven the function f(x) = 270(1.09)* find x when f(x)follow the steps below to show the intersection graph on the computer. [Hint: Use the followingwindow on your graphing calculator: Xmin = -5, Xmax 7, Ymin = 220, Ymax = 415]405 using your graphing calculator. Then1. Write the point of intersection as an ordered pair below. Round the value of a to two decimalplaces.2. Use the Line Tool to draw the Horizontal Line y3. Use the Exponential Tool to draw f(x) = 270(1.09)*.4. Use the Point Tool to identify the point of intersection.405.270(1.09)* = 405Point of Intersection:410400+390+380370+360350+340330320310300290280270260-250-240--5-3-2230-220-

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Answered: Solving Exponential Equations…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter4: Exponential And Logarithmic Functions

Section4.1: Exponential Functions

Problem 46E

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Comparing Exponential Function In these exercises we compare the graphs of two exponential function. Sketch the graph of f(x)=xx/2 and g(x)=3x . Use the laws of Exponents to explain the relationship between these graphs.
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The Rule of 72 This is a continuation of Exercise 14. Financial advisors sometimes use a rule of thumb known as Rule of 72 to get a rough estimate of the time it takes for an investment to double in value. For an investment that is compounded yearly at an interest rate of r%, this rule says it will take about 72/r years for the investment to double. In this calculation, r is the integer interest rate rather than a decimal. Thus, if the interest rate is 8%, we would use 72/8 rather than 72/0.08. For the remainder of this exercise, we will consider an investment that is compounded yearly at an interest rate of 13%. a. According to the Rule 72, how long will it take the investment to double in value? Parts b and c of this exercise will check to see how accurate this estimate is for this particular case. b. Using the answer you got from part a of this exercise, calculate the future value interest factor as defined in Exercise 14. Is it exactly the same as your answer to the part a of Exercise 14? c. If your initial investment was 5000, use your answer from part b to calculate the future value. Did your investment exactly double? Future Value Business and finance texts refer to the value of an investment at a future time as its future value. If an investment of P dollars is compounded yearly at an interest rate of r as a decimal, then the value of the investment after t years is given by FutureValue=P1+rt. In this formula, 1+rt is known as the future value interest factor, so the formula above can be written as FutureValue=PFuturevalueinterestfactor Financial officers normally calculate this or look it up in a table a. What future value interest factor will make an investment double? b. Say you have an investment that is compounded yearly at a rate of 9%. Find the future value interest factor for a 7-year investment. c. Use the results from part b to calculate the 7-year future value if your initial investment is 5000.
Finding pH the hydrogen ion concentrations in cheese range from 4.0x10-7 M tp 1.6x10-5M. Find The corresponding range of pH readings.
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Water Flea F. E. Smith has studied population growth for the water flea. Let N denote the population size. In one experiment, Smith found that G, the rate of growth per day in the population, can be modeled by G=0.44N(228N)228+3.46N a. Draw a graph of G versus N. Include values of N up to 350. b. At what population level does the greatest rate of growth occur? c. There are two values of N where G is zero. Find these values of N and explain what is occurring at these population levels. d. What is the rate of population growth if the population size is 300? Explain what is happening to the population at this level.

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